#### Event Title

### Sub-Jordan Operator Tuples

#### Location

Crow 206

#### Start Date

7-18-2016 5:30 PM

#### End Date

18-7-2016 5:50 PM

#### Description

In this talk we will discuss tuples of 3-isometric and 3-symmetric operators. These operators have connections with Sturm-Liouville theory and are natural generalizations of self-adjoint and isometric operators. We call an operator $J$ a Jordan operator of order $2$ if $J=A+N$, where $A$ is either unitary or self-adjoint, $N$ is nilpotent of order $2$, and $A$ commutes with $N$. As shown in the work of Agler, Ball and Helton, and joint work with McCullough, 3-symmetric and 3-isometric operators are the restriction of a Jordan operator to an invariant subspace. In this talk we discuss the extension of these theorems to the multi-variable case and an application to disconjugacy for Sch{\"o}dinger operators.

Sub-Jordan Operator Tuples

Crow 206

In this talk we will discuss tuples of 3-isometric and 3-symmetric operators. These operators have connections with Sturm-Liouville theory and are natural generalizations of self-adjoint and isometric operators. We call an operator $J$ a Jordan operator of order $2$ if $J=A+N$, where $A$ is either unitary or self-adjoint, $N$ is nilpotent of order $2$, and $A$ commutes with $N$. As shown in the work of Agler, Ball and Helton, and joint work with McCullough, 3-symmetric and 3-isometric operators are the restriction of a Jordan operator to an invariant subspace. In this talk we discuss the extension of these theorems to the multi-variable case and an application to disconjugacy for Sch{\"o}dinger operators.